Preheat oven or Traeger grill to 425F. If using a gas or charcoal grill, set up a 2-zone heat.
Fill a medium sauce pan with water and bring to a boil over high heat. Season the water with a large pinch of salt and add the peas and asparagus. Cook until the vegetables are bright green and slightly tender, around 3 minutes. Transfer them to a bowl of ice water to set the colour and stop the cooking process. Drain completely and set aside.
Season the chicken with 1 teaspoon salt, paprika, and ¼ teaspoon black pepper. Toss to coat.
Preheat a large oven-safe skillet over medium-high heat. Add the avocado oil and heat until shimmering. Add the chicken thighs skin-side down at first. Cook, undisturbed, until the skin is golden brown and crispy, 6 to 8 minutes. Flip and transfer the skillet to the oven or Traeger. If using a gas or charcoal grill, place the skillet over the indirect-heat side. Cook until the thickest part of the chicken registers 165F, around 10 minutes. Remove the chicken from the oven and transfer it to a plate. Cover with foil to keep warm and set aside.
Return the same pan to a medium heat. Discard all but 1 tablespoon of rendered fat. Add the leeks and season with a small pinch of salt. Cook, stirring, until the leeks are slightly softened, around 4 minutes. Add the garlic and cook, stirring, 60 seconds. Add the bone broth, lemon zest, lemon juice, and Dijon mustard. Cook, stirring to incorporate, until reduced in volume by ¼. Add the cold butter and stir quickly to emulsify. Taste for seasoning and adjust with salt, pepper, lemon or mustard, as desired.
Return the peas and asparagus to the pan and toss to coat in the sauce until warmed through. Spoon half of the vegetables onto a serving platter. Arrange the chicken thighs on top and spoon the remaining vegetables and sauce over the chicken. Garnish with fresh chives and dill and serve immediately.